The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 |
Dentro del libro
Resultados 1-5 de 70
Página 11
... vertical or opposite , angles shall be equal . Let the two straight lines AB , CD cut one another in the point E ; the angle AEC shall be equal to the angle DEB , and CEB to AED . C E B D Because the straight line AE makes BOOK I. PROP ...
... vertical or opposite , angles shall be equal . Let the two straight lines AB , CD cut one another in the point E ; the angle AEC shall be equal to the angle DEB , and CEB to AED . C E B D Because the straight line AE makes BOOK I. PROP ...
Página 12
... vertical angles ; therefore the base AB is equal ( 4. 1. ) to the base CF , and the triangle AEB to the triangle CEF , and the remaining angles to the remaining angles , each to each , to which the equal sides are opposite ; wherefore ...
... vertical angles ; therefore the base AB is equal ( 4. 1. ) to the base CF , and the triangle AEB to the triangle CEF , and the remaining angles to the remaining angles , each to each , to which the equal sides are opposite ; wherefore ...
Página 40
... vertically opposite : but BDG is a right angle , because it is equal ( 29. 1. ) to the alternate angle DCE ; therefore the remaining angle DGB is half a right angle , and is therefore equal to the angle DBG ; wherefore also the side BD ...
... vertically opposite : but BDG is a right angle , because it is equal ( 29. 1. ) to the alternate angle DCE ; therefore the remaining angle DGB is half a right angle , and is therefore equal to the angle DBG ; wherefore also the side BD ...
Página 71
... vertical angle of a triangle to construct it in the several cases where the third datum is : - ( a . ) The perpendicular ; ( b . ) The sum of the sides ; ( c . ) The difference of the sides ; ( d . ) One of the angles at the base ...
... vertical angle of a triangle to construct it in the several cases where the third datum is : - ( a . ) The perpendicular ; ( b . ) The sum of the sides ; ( c . ) The difference of the sides ; ( d . ) One of the angles at the base ...
Página 83
... vertical opposite angles BGA , AGF , FGE ; therefore the six angles EGD , DGC , CGB , BGA , AGF , FGE are equal to one another : But equal angles stand upon equal ( 26. 111 ) circumferences ; therefore the six circumferences AB , BC ...
... vertical opposite angles BGA , AGF , FGE ; therefore the six angles EGD , DGC , CGB , BGA , AGF , FGE are equal to one another : But equal angles stand upon equal ( 26. 111 ) circumferences ; therefore the six circumferences AB , BC ...
Otras ediciones - Ver todas
Términos y frases comunes
ABC is equal ABCD angle ABC angle BAC axis bisected centre circle ABC circumference coincide cone conic section construction coordinate planes curve described Descriptive Geometry dicular dihedral angles directrix distance draw edges ellipse equal angles equiangular equimultiples given line given point given straight line greater hence inclination intersection join less Let ABC Let the plane line BC lines drawn magnitudes meet multiple opposite orthograph parabola parallel planes parallelogram parallelopiped perpen perpendicular plane MN plane of projection plane parallel plane PQ prisms profile angles profile plane projecting plane projector Prop Q. E. D. PROPOSITION ratio rectangle rectangle contained rectilineal figure remaining angle respectively right angles SCHOLIUM segment sides six right sphere spherical spherical angle tangent THEOR trace triangle ABC trihedral vertex vertical plane Whence Wherefore
Pasajes populares
Página 19 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Página 35 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Página 4 - AB; but things which are equal to the same are equal to one another...
Página 128 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Página 8 - If two triangles have two sides of the one equal to two sides of the...
Página 36 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced...
Página 21 - BCD, and the other angles to the other angles, (4. 1.) each to each, to which the equal sides are opposite : therefore the angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal to one another, AC is parallel (27. 1 .) to DB ; and it was shown to be equal to it. Therefore straight lines, &c.
Página 65 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the circle.
Página 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Página 116 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.